When you dilate a figure with a scale factor of one half, each side length is multiplied by the scale factor.
In this case, if you have a rectangle with side lengths of 12 and 4, and dilate it with a scale factor of one half, the resulting image would have side lengths of:
12 * 1/2 = 6
4 * 1/2 = 2
Therefore, the side lengths of the resulting image would be 6 and 2.
What if you had a rectangle with side lengths of 12 and 4, and dilated it with a scale factor of one half? What would be the side lengths of the resulting image?
7 answers
When a pre-image is dilated, is the resulting image congruent to the original? Do dilations maintain isometry? Explain.
No, when a pre-image is dilated, the resulting image is not congruent to the original.
A dilation changes the size of a figure, but not its shape. It scales the figure up or down uniformly, either expanding it or shrinking it. This means that the resulting image will have different dimensions compared to the original image, except in the special case of a dilation with a scale factor of 1, which results in a congruent image.
Dilations do not maintain isometry, which means they do not preserve distances and angles. The distances between points in the original figure are not preserved in the resulting image. For example, a dilation with a scale factor greater than 1 will increase the distance between points in the image, while a dilation with a scale factor less than 1 will decrease the distance between points. Additionally, dilations do not preserve angles, as the angles in the image will be different from those in the original figure.
In summary, dilations change the size of a figure but not its shape, and they do not maintain isometry.
A dilation changes the size of a figure, but not its shape. It scales the figure up or down uniformly, either expanding it or shrinking it. This means that the resulting image will have different dimensions compared to the original image, except in the special case of a dilation with a scale factor of 1, which results in a congruent image.
Dilations do not maintain isometry, which means they do not preserve distances and angles. The distances between points in the original figure are not preserved in the resulting image. For example, a dilation with a scale factor greater than 1 will increase the distance between points in the image, while a dilation with a scale factor less than 1 will decrease the distance between points. Additionally, dilations do not preserve angles, as the angles in the image will be different from those in the original figure.
In summary, dilations change the size of a figure but not its shape, and they do not maintain isometry.
Instead of referring to these triangles as congruent, these triangles are best described as "similar". What do you think the geometric term, similar, means?
You are correct, when the pre-image is dilated, the resulting image is best described as "similar" rather than "congruent".
In geometry, similarity refers to a relationship between two figures that have the same shape but possibly different sizes. When two figures are similar, their corresponding angles are equal and their corresponding side lengths are proportional. However, the corresponding side lengths of similar figures are not necessarily equal.
This concept of similarity allows us to compare and analyze figures, even if they have different sizes. It is often represented using the symbol ~ (tilde) between two figures, such as triangle ABC ~ triangle DEF, which means that the two triangles are similar.
Similarity is an important property in geometry as it helps in solving problems involving scaling, enlargement, and reduction of figures, as well as in trigonometry and fractal geometry.
In geometry, similarity refers to a relationship between two figures that have the same shape but possibly different sizes. When two figures are similar, their corresponding angles are equal and their corresponding side lengths are proportional. However, the corresponding side lengths of similar figures are not necessarily equal.
This concept of similarity allows us to compare and analyze figures, even if they have different sizes. It is often represented using the symbol ~ (tilde) between two figures, such as triangle ABC ~ triangle DEF, which means that the two triangles are similar.
Similarity is an important property in geometry as it helps in solving problems involving scaling, enlargement, and reduction of figures, as well as in trigonometry and fractal geometry.
will you summ it up pleaee?
Certainly! Here's a summary:
In geometry, when two figures are similar, it means they have the same shape but possibly different sizes. Their corresponding angles are equal, and their corresponding side lengths are proportional. However, the corresponding side lengths of similar figures are not necessarily equal. Similarity is denoted by the ~ (tilde) symbol between the names of the figures. This concept is important for comparing and analyzing figures, solving scaling problems, and studying trigonometry and fractal geometry.
In geometry, when two figures are similar, it means they have the same shape but possibly different sizes. Their corresponding angles are equal, and their corresponding side lengths are proportional. However, the corresponding side lengths of similar figures are not necessarily equal. Similarity is denoted by the ~ (tilde) symbol between the names of the figures. This concept is important for comparing and analyzing figures, solving scaling problems, and studying trigonometry and fractal geometry.
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